Question

All lines 1 unit distant from the origin ANS. (xy'-y)^2 = (1 + (y')^2)

Answer 1

@ganeshie8

Answer 2

helo guys

Answer 3

help please

Answer 4

you have multiple post

Answer 5

http://openstudy.com/study#/updates/55a88316e4b0c25fa1567648

Answer 6

what is the question here?

Answer 7

Just a guess: Find an ODE whose general solution is the family of curves that satisfy some property. What that property might be, I'm not so sure. "All lines 1 unit distant from the origin" ? idk what to make of that.

Answer 8

well, those are just tangent lines to \(x^2+y^2=1\), so $$2x+2yy'=0\\x+yy'=0\\y'=-\frac{x}y$$so \(\dfrac{dy}{dx}=-\dfrac{x_0}{y_0}\) which gives $$\frac{y-y_0}{x-x_0}=-\frac{x_0}{y_0}$$